def quatAverageCluster(q_in, qsym):
"""
"""
from symmetry import toFundamentalRegion
assert q_in.ndim == 2, "input must be 2-s hstacked quats"
# renormalize
q_in = unitVector(q_in)
# check to see num of quats is > 1
if q_in.shape[1] < 3:
if q_in.shape[1] == 1:
q_bar = q_in
else:
ma, mq = misorientation(q_in[:, 0].reshape(4, 1), q_in[:, 1].reshape(4, 1), (qsym,))
q_bar = quatProduct(q_in[:, 0].reshape(4, 1), quatOfExpMap(0.5 * ma * unitVector(mq[1:].reshape(3, 1))))
else:
# use first quat as initial guess
phi = 2.0 * arccos(q_in[0, 0])
if phi <= finfo(float).eps:
x0 = zeros(3)
else:
n = unitVector(q_in[1:, 0].reshape(3, 1))
x0 = phi * n.flatten()
# first drag to origin using first quat (arb!)
q0 = q_in[:, 0].reshape(4, 1)
qrot = dot(quatProductMatrix(invertQuat(q0), mult="right"), q_in)
# second, re-cast to FR
qrot = toFundamentalRegion(qrot.squeeze(), crysSym=qsym)
# compute arithmetic average
q_bar = unitVector(average(qrot, axis=1).reshape(4, 1))
# unrotate!
q_bar = dot(quatProductMatrix(q0, mult="right"), q_bar)
# re-map
q_bar = toFundamentalRegion(q_bar, crysSym=qsym)
return q_bar
def quatAverageCluster(q_in, qsym):
"""
"""
from symmetry import toFundamentalRegion
assert q_in.ndim == 2, 'input must be 2-s hstacked quats'
# renormalize
q_in = unitVector(q_in)
# check to see num of quats is > 1
if q_in.shape[1] < 3:
if q_in.shape[1] == 1:
q_bar = q_in
else:
ma, mq = misorientation(q_in[:, 0].reshape(4, 1),
q_in[:, 1].reshape(4, 1), (qsym,))
q_bar = quatProduct(
q_in[:, 0].reshape(4, 1),
quatOfExpMap(0.5*ma*unitVector(mq[1:].reshape(3, 1)))
)
else:
# first drag to origin using first quat (arb!)
q0 = q_in[:, 0].reshape(4, 1)
qrot = dot(
quatProductMatrix(invertQuat(q0), mult='left'),
q_in)
# second, re-cast to FR
qrot = toFundamentalRegion(qrot.squeeze(), crysSym=qsym)
# compute arithmetic average
q_bar = unitVector(average(qrot, axis=1).reshape(4, 1))
# unrotate!
q_bar = dot(
quatProductMatrix(q0, mult='left'),
q_bar)
# re-map
q_bar = toFundamentalRegion(q_bar, crysSym=qsym)
return q_bar
def quatAverageCluster(q_in, qsym):
"""
"""
from symmetry import toFundamentalRegion
assert q_in.ndim == 2, 'input must be 2-s hstacked quats'
# renormalize
q_in = unitVector(q_in)
# check to see num of quats is > 1
if q_in.shape[1] < 3:
if q_in.shape[1] == 1:
q_bar = q_in
else:
ma, mq = misorientation(q_in[:, 0].reshape(4, 1),
q_in[:, 1].reshape(4, 1), (qsym,))
q_bar = quatProduct(q_in[:, 0].reshape(4, 1),
quatOfExpMap(0.5*ma*unitVector(mq[1:].reshape(3, 1))))
else:
# first drag to origin using first quat (arb!)
q0 = q_in[:, 0].reshape(4, 1)
qrot = dot(
quatProductMatrix( invertQuat( q0 ), mult='left' ),
q_in)
# second, re-cast to FR
qrot = toFundamentalRegion(qrot.squeeze(), crysSym=qsym)
# compute arithmetic average
q_bar = unitVector(average(qrot, axis=1).reshape(4, 1))
# unrotate!
q_bar = dot(
quatProductMatrix( q0, mult='left' ),
q_bar)
# re-map
q_bar = toFundamentalRegion(q_bar, crysSym=qsym)
return q_bar
def discreteFiber(c, s, B=I3, ndiv=120, invert=False, csym=None, ssym=None):
"""
"""
import symmetry as S
ztol = 1.e-8
# arg handling for c
if hasattr(c, '__len__'):
if hasattr(c, 'shape'):
assert c.shape[0] == 3, \
'scattering vector must be 3-d; yours is %d-d' \
% (c.shape[0])
if len(c.shape) == 1:
c = c.reshape(3, 1)
elif len(c.shape) > 2:
raise RuntimeError, \
'incorrect arg shape; must be 1-d or 2-d, yours is %d-d' \
% (len(c.shape))
else:
# convert list input to array and transpose
if len(c) == 3 and isscalar(c[0]):
c = asarray(c).reshape(3, 1)
else:
c = asarray(c).T
else:
raise RuntimeError, 'input must be array-like'
# arg handling for s
if hasattr(s, '__len__'):
if hasattr(s, 'shape'):
assert s.shape[0] == 3, \
'scattering vector must be 3-d; yours is %d-d' \
% (s.shape[0])
if len(s.shape) == 1:
s = s.reshape(3, 1)
elif len(s.shape) > 2:
raise RuntimeError, \
'incorrect arg shape; must be 1-d or 2-d, yours is %d-d' \
% (len(s.shape))
else:
# convert list input to array and transpose
if len(s) == 3 and isscalar(s[0]):
s = asarray(s).reshape(3, 1)
else:
s = asarray(s).T
else:
raise RuntimeError, 'input must be array-like'
nptc = c.shape[1]
npts = s.shape[1]
c = unitVector(dot(B, c)) # turn c hkls into unit vector in crys frame
s = unitVector(s) # convert s to unit vector in samp frame
retval = []
for i_c in range(nptc):
dupl_c = tile(c[:, i_c], (npts, 1)).T
ax = s + dupl_c
anrm = columnNorm(ax).squeeze() # should be 1-d
okay = anrm > ztol
nokay = okay.sum()
if nokay == npts:
ax = ax / tile(anrm, (3, 1))
else:
nspace = nullSpace(c[:, i_c].reshape(3, 1))
hperp = nspace[:, 0].reshape(3, 1)
if nokay == 0:
ax = tile(hperp, (1, npts))
else:
ax[:, okay] = ax[:, okay] / tile(anrm[okay], (3, 1))
ax[:, not okay] = tile(hperp, (1, npts - nokay))
q0 = vstack( [ zeros(npts), ax ] )
# find rotations
# note: the following line fixes bug with use of arange with float increments
phi = arange(0, ndiv) * (2*pi/float(ndiv))
qh = quatOfAngleAxis(phi, tile(c[:, i_c], (ndiv, 1)).T)
# the fibers, arraged as (npts, 4, ndiv)
qfib = dot( quatProductMatrix(qh, mult='right'), q0 ).transpose(2, 1, 0)
if csym is not None:
retval.append(S.toFundamentalRegion(qfib.squeeze(),
crysSym=csym,
sampSym=ssym))
else:
retval.append(fixQuat(qfib).squeeze())
return retval
def discreteFiber(c, s, B=I3, ndiv=120, invert=False, csym=None, ssym=None):
"""
"""
import symmetry as S
ztol = 1.e-8
# arg handling for c
if hasattr(c, '__len__'):
if hasattr(c, 'shape'):
assert c.shape[0] == 3, \
'scattering vector must be 3-d; yours is %d-d' \
% (c.shape[0])
if len(c.shape) == 1:
c = c.reshape(3, 1)
elif len(c.shape) > 2:
raise RuntimeError, \
'incorrect arg shape; must be 1-d or 2-d, yours is %d-d' \
% (len(c.shape))
else:
# convert list input to array and transpose
if len(c) == 3 and isscalar(c[0]):
c = asarray(c).reshape(3, 1)
else:
c = asarray(c).T
else:
raise RuntimeError, 'input must be array-like'
# arg handling for s
if hasattr(s, '__len__'):
if hasattr(s, 'shape'):
assert s.shape[0] == 3, \
'scattering vector must be 3-d; yours is %d-d' \
% (s.shape[0])
if len(s.shape) == 1:
s = s.reshape(3, 1)
elif len(s.shape) > 2:
raise RuntimeError, \
'incorrect arg shape; must be 1-d or 2-d, yours is %d-d' \
% (len(s.shape))
else:
# convert list input to array and transpose
if len(s) == 3 and isscalar(s[0]):
s = asarray(s).reshape(3, 1)
else:
s = asarray(s).T
else:
raise RuntimeError, 'input must be array-like'
nptc = c.shape[1]
npts = s.shape[1]
c = unitVector(dot(B, c)) # turn c hkls into unit vector in crys frame
s = unitVector(s) # convert s to unit vector in samp frame
retval = []
for i_c in range(nptc):
dupl_c = tile(c[:, i_c], (npts, 1)).T
ax = s + dupl_c
anrm = columnNorm(ax).squeeze() # should be 1-d
okay = anrm > ztol
nokay = okay.sum()
if nokay == npts:
ax = ax / tile(anrm, (3, 1))
else:
nspace = nullSpace(c[:, i_c].reshape(3, 1))
hperp = nspace[:, 0].reshape(3, 1)
if nokay == 0:
ax = tile(hperp, (1, npts))
else:
ax[:, okay] = ax[:, okay] / tile(anrm[okay], (3, 1))
ax[:, not okay] = tile(hperp, (1, npts - nokay))
q0 = vstack([zeros(npts), ax])
# find rotations
# note: the following line fixes bug with use of arange with float increments
phi = arange(0, ndiv) * (2 * pi / float(ndiv))
qh = quatOfAngleAxis(phi, tile(c[:, i_c], (ndiv, 1)).T)
# the fibers, arraged as (npts, 4, ndiv)
qfib = dot(quatProductMatrix(qh, mult='right'), q0).transpose(2, 1, 0)
if csym is not None:
retval.append(
S.toFundamentalRegion(qfib.squeeze(),
crysSym=csym,
sampSym=ssym))
else:
retval.append(fixQuat(qfib).squeeze())
return retval